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The debate between the grouping of this disorder is very interesting. Psychologists dont know if its more related to drug addictions or self harming practices.

Another philosopher that performed a deep examination the shape and motion of the earth and celestial bodies was Claudius Ptolemy. He worked at the museum, or instructional center, school and library of manuscripts in Alexandria. Ptolemy is responsible for a lot of concepts, but one of his most famous works summarizing these concepts is the Almagest, a work in 13 books where he presented his astronomical theories. Ptolemy discussed the idea of epicycles and center of the world. The epicycle center moves at a constant rate in a counter clockwise direction. Once other celestial bodies, such as the planets, were introduced into this system, it became more complex. The models for Jupiter, Saturn, and Mars included the center of the circle, the equant point, the epicycle, and an observer from earth to give perspective. The discovery of this model was that the center of the Mercury and Venus epicycles must always be colinear with the sun. This assures of bounded elongation. (Bowler, 2010, 48) Bounded elongation is the angular distance of celestial bodies from the center of the universe. Ptolemy’s model of the cosmos and his studies landed him an important place in history in the development of modern day science. The cosmos was a concept further developed by Ptolemy that included equant circles, however Copernicus model of the universe was simpler. In the Ptolemaic system, the earth was at the center of the universe with the moon, the sun, and five planets circling it. The circle of fixed stars marked the outermost sphere of the universe and beyond that would be the philosophical “aether” realm. The earth was at the exact center of the cosmos, most likely because people at the time believed the earth had to be at the center of the universe because of the deductions made by observers in the system. The sphere carrying the moon is described as the boundary between the corruptible and changing sublunary world and the incorruptible and unchanging heavens above it (Bowler, 2010, 26). The heavens were defined as incorruptible and unchanging based on theology and mythology of the past. The Almagest introduced the idea of the sphericity of heavens. The assumption is that the sizes and mutual distances of the stars must appear to vary however one supposes the earth to be positioned, yet no such variation occurred (Bowler 55), The aether is the area that describes the universe above the terrestrial sphere. This component of the atmosphere is unknown and named by philosophers, though many do not know what lies beyond the realm of what has been seen by human beings. The aether is used to affirm the sphericity of the heavens and this is confirmed by the belief that different shapes have an equal boundary and those with more angles are greater, the circle is greater than all other surfaces, and a sphere greater than all other solids. Therefore, through physical considerations, and heavenly philosophy, there is an assumption that the heavens must be spherical. The Almagest also suggested that the earth was spherical because of similar philosophy. The differences in the hours across the globe are proportional to the distances between the spaces at which they are being observed. Therefore, it can be deduced that the earth is spherical because of the evenly curving surface and the differences in time that was constant and proportional. In laymen terms, the earth must be spherical because they change in time-zones across the world occur in a uniform fashion, as with the rotation of a sphere. The observation of eclipses further confirmed these findings because everyone on earth could see a lunar eclipse, for example, but it would be at different hours.

The Almagest also suggest that the earth is at the center of the universe. The basis on which this is found is in the fact that six zodiac signs can be seen above earth, while at the same time the other signs are not visible (Bowler 57). The way that we observe the increase and decrease of daylight would be different if the earth was not at the center of the universe. Though this view later proofed to be invalid, this was a good proponent to the discussion of the design of the universe. Ideas on the universe were later developed and advanced through the works of other astronomers such as Copernicus, who built on ideas through his knowledge of the world and God.

Bowler, Peter J., and Iwan Rhys Morus. Making Modern Science: A Historical Survey. Chicago, IL: Univ. of Chicago Press, 2010.

Works [edit] Theodosius most recognized work was a compilation of three-volume text on spherical geometry, Sphaerica (translated Sphaerics), which satisfied the need for astronomers of the time to tackle the subject of sphericity. There have been many debates over the success and credibility of this book because while it does provide valuable information on everything spherical, many would argue that it contains almost no original philosophy from Theodosius. The Mathematician, T. Heath called him a “laborious compiler” and Otto Neugebauer pointed out that his theories seldom treat more than what is obvious and his proofs do little more than reword the conjecture.12 Another notable fact is that Theodosius left out the great-circle triangle, which was an important structure at the time and still remains as so today. Throughout the compilation, he rarely admits to the assumptions used and the composition of the ideas. Nonetheless, despite criticism, this text did exactly what Theodosius aimed for it to and that was explain the phenomenon of spherical geometry. The thoughts he compiles are well-organized and serve the purpose of responding to the need of one text that contains all information about this science.

12 Kwan, A. (1970, January 01). Theodosius of Bithynia. Retrieved November 12, 2018.

13 file:///C:/Users/D.Hervey/AppData/Local/Packages/Microsoft.MicrosoftEdge_8wekyb3d8bbwe/TempState/Downloads/25991-Article%20Text-57821-1-10-20151116%20(3).pdf Berggren, L. (2012). Book Review: The Spherics of Theodosius, Theodosius, Sphaerica: Arabic and Medieval Latin TranslationsTheodosius, Sphaerica: Arabic and Medieval Latin Translations. Edited by KunitzschPaul and LorchRichard (Boethius, lxii; Franz Steiner Verlag, Stuttgart, 2010). Pp. 431. €64. ISBN 978-3-515-09288-3. Journal for the History of Astronomy, 43(2), 250-252. doi:10.1177/002182861204300214

On Pythagorean Harmony Theon was a great philosopher of harmony and he discusses semitones in his treatise. There are several semitones used in greek music, but of this variety, there are two that are very common. The “diatonic semitone” with a value of 16/15 and the “chromatic semitone” with a value of 25/24 are the two more commonly used semitones. In these times, pythagoreans did not rely on irrational numbers for understanding of harmonies and the logarithm for these semitones did not match with their philosophy. Their logarithms did not lead to irrational numbers, however Theon tackled this discussion head on. He acknowledged that “one can prove that” the tone of value 9/8 cannot be divided into equal parts and so it is a number in itself. Many pythagoreans believed in the existence of irrational numbers, but did not believe in using them because they were unnatural and not positive integers. Theon also does an amazing job of relating quotients of integers and musical intervals. He illustrates this idea in his writings and through experiments. He discusses the pythagoreans method of looking at harmonies and consonances through half-filling vases and explains these experiments on a deeper level focusing on the fact that the octaves, fifths, and fourths correspond respectively with the fractions 2/1, 3/2, and and 4/3. His contributions greatly contributed to the fields of music and physics.

15 apadopoulos, A. (2002). Mathematics and music theory: From pythagoras to rameau. The Mathematical Intelligencer, 24(1), 65-73. doi:10.1007/bf03025314